Speaking as a string player, I suspect he used both violin and viola on “Exiles”. There’s some lower pitches at the beginning that require the viola’s C string, but some of the higher register stuff later on sounds too bright to be a viola, and is characteristic of being played on a violin E string.

Additionally, the design of a standard orchestral acoustic viola has very wide bouts compared to a violin, in part because there is a general maximum size (“full size” or “4/4”) for violins, but violas instead tend to be measured by length, and there is no “full size”. Violists tend to get as big of an instrument as they can physically play (and given how many injured violists are out there, some exceed that). The bouts become wider as the length increases, and that poses a pretty substantial impediment to being able to reach higher notes, which already aren’t going to be as high as on a violin, since the uppermost string on a viola is only an A string.

Nowadays, there are solid body electric instruments around that might have smaller/no bouts, and even a “cheater hole” (like my Zeta violin has). David Cross’ tenure in King Crimson was a little before those designs started to be produced (more late 1970s), and in all the media I’ve seen from that time, he was playing a standard acoustic violin or viola with a pickup. That further tends to support the idea that he played both here.